It is well known to grind spur and helical gears with threaded grinding wheels to produce crowned tooth surfaces in the lengthwise (longitudinal) direction. Crowning in such a manner relieves end loading by effectively moving the area of contact away from the tooth ends and toward the center of the tooth.
On a threaded wheel grinding machine, the conventional method used to produce lengthwise crowning on spur gears involves changing the relative distance between the gear and grinding wheel axes as the grinding wheel moves over the gear face, (stroke motion). This relative distance is reduced near the ends of the gear face, thus thinning the gear teeth as more stock material is removed at the tooth ends. As the grinding wheel moves inward from the tooth ends, the relative distance between the gear and grinding wheel is increased to remove less stock material and provide the desired tooth thickness at or near the mid-face position, where the gear tooth flanks are normally expected to contact the mating member.
The conventional method of producing lengthwise crowning is generally effective for gears where the axial arrangement between workpiece and tool is close to 90 degrees, i.e. for spur and low helix angle gears. However, this method produces potentially detrimental flank form distortions on helical gears which require a crossed axis angle deviating significantly from 90 degrees. The flank distortions are caused by uneven stock removal, which progressively alters the pressure angle of the tooth flanks along the tooth length, and is most severe at the tooth ends. The tooth flanks appear to be twisted in the lengthwise direction, and thus the condition is known as "flank twist." It is well known that the magnitude of the flank twist becomes more pronounced with increasing helix angle, increasing lengthwise crowning, and decreasing pressure angle, among other factors.
Most spur and helical gears are inspected for profile (involute) form errors only at one location in the tooth lengthwise direction, which usually corresponds to the mid face position. Lead (longitudinal) form errors are typically checked only at one profile height, which normally corresponds to the pitch cylinder. Flank twist errors cannot be determined from inspection data collected in this manner. Thus, although flank twist is generally well known in theory, it is frequently ignored or remains undetected in practice. However, on helical gears with crowning, the flank twist effect can be significant, and may adversely affect one or more of the following characteristics: backlash, motion transmission error, noise, or strength. Conversely, it may be desirable to produce flank twist to improve or modify any of the aforementioned characteristics on spur gears or on helical gears with no lengthwise crowning, where flank twist effects would otherwise be small.
One method for addressing flank twist is disclosed in U.S. Pat. No. 4,850,155 to Sulzer. In this method, the pressure angle and tooth thickness of the tool change continuously from one end of the tool toward the other. The motion of the tool with respect to the workpiece is axial and tangential, which results in a diagonal feeding of the workpiece across the tool. As the tool is fed along the gear face, it is moved tangentially so as to expose the workpiece to the portion of the tool with the pressure angle modification required to correct flank twist errors. Tooth thickness changes along the tool length serve in a similar manner to produce the desired lengthwise crowning, which may occur in concert with the earlier explained machine motions normally used to effect crowning. For clarity, FIG. 1 compares the conventional generating rack with that of the Sulzer method and illustrates the pressure angle change along the length of the generating tool according to Sulzer. FIG. 2 shows an enlargement of the same for two teeth at either end of the tool.
Although capable of producing tooth twist modification, the Sulzer method has significant practical limitations. In the case of a threaded grinding machine with conventional wheel dressing mechanism, it is not practical (and in most cases not possible) to dress a wheel with continuously changing pressure angle. In the case of gear hobbing, the hob profile grinding operation becomes excessively complex.
Another method of alleviating the distortions of flank twisting is disclosed by Schriefer in "Continuous CNC Gear Grinding", The Gleason Works, March 1996. In this disclosure, it is suggested that the tooth trace produced by a threaded grinding wheel passing over the face of a helical workpiece becomes distorted because the straight generation front of the tool lies at an angle to the workpiece axis. With this arrangement, the actual crown envelope surface is distorted with respect to the desired crown envelope surface, thus producing tooth flank deviations. Schriefer proposes providing an elliptically crowned grinding wheel to negate the effects of flank twisting. The elliptical shape results from passing an axial crossing plane through a cylinder representing the desired circular lead crowning of the tooth surfaces of the workpiece.
The method proposed by Schriefer also has significant practical limitations. Although an elliptical shape could be produced on a threaded grinding wheel using modern CNC dressing mechanisms, the continuously changing curvature of the ellipse is very sensitive to relative positioning errors between the dresser and wheel. For the same reason, the process is also excessively sensitive to positioning errors between the wheel and workpiece during grinding. It is furthermore not straightforward to use a tool with given elliptical shape for different tooth twist modification amounts. This represents a limitation primarily for non-dressable wheels or hobbing tools, where a physically different tool would be required for different flank twist modifications on a given workpiece. Besides these limitations, Schriefer does not disclose the relationship between the tool width, machine motions, and elliptical shape of the generating front, which would be central to a flank twist modification technique.